Self-consistent HF Research Articles

Tetrahedral symmetry in the ground state of 16O

Based on the Skyrme energy density functional, the self-consistent HF calculations have been performed for 16O, and the results show that the double point group tetrahedral symmetry TdD may play an important role in the configuration of many-body fermion system in the ground state of 16O. The corresponding total density distribution in the ground state, calculated by using the HF wave functions, presents the distinct 4α cluster-like tetrahedral structure with the Td symmetry. Among others, the necessary restoration of the rotational and parity symmetry, plays a crucial role for the occurrence of the tetrahedral symmetry in 16O.

Precision of finite-difference representation in 3D coordinate-space Hartree-Fock-Bogoliubov calculations

The current work plans to study the accuracy due to FD approximation to the 3D nuclear HFB problem. By (1) taking the wave functions solved in harmonic oscillator (HO) basis, (2) representing the HFB problem in coordinate space using FD method, the current work carefully evaluates the error due to box discretization by examining the deviation of the resulted HFB matrix, the total energies in the coordinate space, from those calculated with HO method, the latter of which is free from numerical error within its model configuration. To estimate how the error (given by the box discretization schemes suggested above) accumulates with self-consistent iterations, self-consistent HF and HFB calculations (with two-basis method) has been carried out for doubly magic nuclei, $^{40}$Ca, $^{132}$Sn, and $^{110}$Mo. The resulted total energies are compared with those of HO basis, and 3D coordinate space calculations in literatures. The analysis shows that, for grid spacing $\le$0.6\,fm, the off-diagonal elements of the resulted HFB matrix elements (M.E.) are extremely small ($<$1\,keV). The resulted quasi-particle (q.p.) spectra differ from those of HO calculations by a few keV. Self-consistent HF and HFB calculations within the current FD method with the above box discretizatioin schemes give results similar to those calculations of existing HO basis, and coordinate space method.

Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies.

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning's correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study. It is known that even the very expensive X = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4 to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules.

Analysis of the neutron and proton contributions to the pygmy dipole mode in doubly magic nuclei

Abstract The electric dipole excitations are investigated in the framework of the self-consistent HF + RPA approximation with Skyrme interactions. Magic O, Ca, Ni and Sn isotopes are used to investigate low-lying modes. Neutron and proton transition densities analysis of each nucleus is provided to examine the behavior of Pygmy Dipole Resonance (PDR) of nuclei under excitation, showing a complex pattern along the nuclear chart. The PDR in the very neutron-rich 70 Ca nucleus exhibits a novel mode of excitation, the so-called arch mode. The collectivity of the PDR is also analysed.

What can we learn from recent non-relativistic mean field calculations ?

In the present contribution, we discuss the relevance of fully self-consistent HF plus RPA (or HF-BCS plus QRPA) calculations based on Skyrme effective forces, and their impact on our present knowledge of basic properties of the nuclear equation of state, like the incompressibilty and the symmetry energy. Finally, we address the problem whether correlations beyond mean field can alter the picture obtained at the (Q)RPA level. Throghout the paper, the comparison with the results obtained using Gogny forces, or RMF Lagrangians, will be emphasized.

Effect of large neutron excess in the region of the giant dipole and quadrupole resonance

We study the dipole and quadrupole modes of neutron rich nuclei within the selfconsistent HF + RPA. The presence of neutron skin enhances the mixing of isoscalar and isovector modes. Then it is possible to excite modes of isovector character by an isoscalar probe. In particular we analize the excitation of dipole modes by alpha scattering. The excitation of compressional isoscalar mode is also studied.

Ground-state correlations beyond RPA

An approach is proposed which includes ground-state correlations beyond RPA. This is achieved by using a renormalized quasiboson approximation with reference to the correlated ground-state of the system, rather than to the uncorrelated Hartree-Fock one, and by expressing the particle-particle and hole-hole pair operators in terms of the particle-hole ones. The set of the so-obtained nonlinear equations for the one-phonon energy and amplitudes are first solved within the Lipkin-Meshkov-Glick model and the results are compared with those of previous approaches as well as with the exact ones. Applications to realistic nuclei, starting from fully self-consistent HF + RPA calculations with a Skyrme force are also presented.

The RPA nuclear continuum in16O(e, e?) reactions at low momentum transfer decay on (e, e?p) and (e, e?n) reaction channels

A theoretical investigation has been performed of16O(e, e′) and16O(e, e′x) reactions at low momentum transfer in the frame of a self-consistent HF and RPA theory with a SK3 interaction. Nuclear responses and their multipole components have been calculated in the whole energy-range for the two electron kinematicsi) ɛ i =67 MeV and θ=40°,ii) ɛ i =130 MeV and θ=50°. The microscopic structure of HF and RPA resonating states in the energy continuum has been inferred from the calculation. Decay properties in the reaction channels (e, e′p) and (e, e′n) have been discussed in the two cases of a semidirect and a knockout reaction process.